The formula to calculate the edge length of a regular polygon given the circumradius is:
\[ l_e = 2 \cdot r_c \cdot \sin\left(\frac{\pi}{N_S}\right) \]
Where:
The edge length of a regular polygon is the length of one of the sides of the polygon.
The circumradius of a regular polygon is the radius of a circumcircle touching each of the polygon's vertices.
The number of sides of a regular polygon denotes the total number of sides of the polygon. The number of sides is used to classify the types of polygons.
Let's assume the following values:
Using the formula:
\[ l_e = 2 \cdot 13 \cdot \sin\left(\frac{\pi}{8}\right) = 9.94976924 \text{ m} \]
The edge length is approximately 9.94976924 meters.
| Circumradius (m) | Number of Sides | Edge Length (m) |
|---|---|---|
| 10 | 5 | 11.75570505 |
| 10 | 6 | 10.00000000 |
| 10 | 7 | 8.67767478 |
| 10 | 8 | 7.65366865 |
| 10 | 9 | 6.84040287 |
| 10 | 10 | 6.18033989 |
| 12 | 5 | 14.10684606 |
| 12 | 6 | 12.00000000 |
| 12 | 7 | 10.41320974 |
| 12 | 8 | 9.18440238 |
| 12 | 9 | 8.20848344 |
| 12 | 10 | 7.41640786 |
| 14 | 5 | 16.45798706 |
| 14 | 6 | 14.00000000 |
| 14 | 7 | 12.14874470 |
| 14 | 8 | 10.71513611 |
| 14 | 9 | 9.57656401 |
| 14 | 10 | 8.65247584 |
| 16 | 5 | 18.80912807 |
| 16 | 6 | 16.00000000 |
| 16 | 7 | 13.88427965 |
| 16 | 8 | 12.24586984 |
| 16 | 9 | 10.94464459 |
| 16 | 10 | 9.88854382 |
| 18 | 5 | 21.16026908 |
| 18 | 6 | 18.00000000 |
| 18 | 7 | 15.61981461 |
| 18 | 8 | 13.77660357 |
| 18 | 9 | 12.31272516 |
| 18 | 10 | 11.12461180 |
| 20 | 5 | 23.51141009 |
| 20 | 6 | 20.00000000 |
| 20 | 7 | 17.35534956 |
| 20 | 8 | 15.30733729 |
| 20 | 9 | 13.68080573 |
| 20 | 10 | 12.36067977 |